Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations

Xun Li, Jingrui Sun, Jie Xiong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)


The optimality system, which is a linear mean-field forward–backward stochastic differential equation with constraint, is obtained by a variational method. By decoupling the optimality system, two coupled Riccati equations and an MF-BSDE are derived. It turns out that the coupled two Riccati equations are uniquely solvable. Then a complete and explicit representation is obtained for the optimal control.
Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalApplied Mathematics and Optimization
Publication statusAccepted/In press - 7 Dec 2017


  • Decoupling
  • Linear quadratic optimal control
  • Mean-field backward stochastic differential equation
  • Optimality system
  • Riccati equation

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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